Related papers: Pfaffian-based topological invariants for one dime…
We present generic conditions for phase band crossings for a class of periodically driven integrable systems represented by free fermionic models subjected to arbitrary periodic drive protocols characterized by a frequency $\omega_D$. These…
We prove the Pfaffian Sign Theorem for the dimer model on a triangular lattice embedded in the torus. More specifically, we prove that the Pfaffian of the Kasteleyn periodic-periodic matrix is negative, while the Pfaffians of the Kasteleyn…
We theoretically consider transport properties of a normal metal (N)- superconducting semiconductor nanowire (S)-normal metal (N) structure (NSN) in the context of the possible existence of Majorana bound states in disordered…
We introduce exactly solvable models of interacting (Majorana) fermions in $d \ge 3$ spatial dimensions that realize a new kind of topological quantum order, building on a model presented in ref. [1]. These models have extensive topological…
We present measurements and simulations of semiconductor-superconductor heterostructure devices that are consistent with the observation of topological superconductivity and Majorana zero modes. The devices are fabricated from high-mobility…
Topological magnetic structures, such as Hopfions, are central to three-dimensional magnetism, but their characterization in complex geometries remains challenging. We introduce a robust finite-element method for calculating the Hopf index…
We investigate persistent currents in metallic rings interrupted by a Coulomb blockaded topological superconducting segment. We show that the presence of Majorana bound states in the superconductor is reflected in the emergence of an h/e…
In this general article, we map the one-dimensional transverse field quantum Ising model of ferromagnetism to Kitaev's one-dimensional p-wave superconductor, which has its application in fault-tolerant topological quantum computing. Mapping…
We show how the $\mathbb{Z}_{2}$ topological index of a one-dimensional topological p-wave superconductor can be revealed when driving with a classical vector potential i.e. an electromagnetic wave, through the light-induced transition…
Quantum Hall bilayers are a uniquely tunable platform that can realize continuous transitions between distinct topological phases of matter. One prominent example is the transition between the Halperin state and the Moore--Read Pfaffian,…
We study theoretically the electrical current and low-frequency noise for a linear Josephson junction structure on a topological insulator, in which the superconductor forms a closed ring and currents are injected from normal regions inside…
We demonstrate that in two-dimensional noncentrosymmetric s-wave superconductors under applied magnetic fields for a particular electron density, topological order emerges, and there exists a zero energy Majorana fermion mode in a vortex…
The Z2 topological invariant is defined in the chiral d-wave superconductor having a triangular lattice in the presence of the 120 degrees magnetic ordering. By analyzing the Z2 invariant, we determine the conditions of implementing…
Majorana zero modes in a superconductor-semiconductor nanowire have been extensively studied during the past decade. Disorder remains a serious problem, preventing the definitive observation of topological Majorana bound states. Thus, it is…
A phenomenological Hamiltonian of a closed (i.e., unitary) quantum system is assumed to have an $N$ by $N$ real-matrix form composed of a unperturbed diagonal-matrix part $H^{(N)}_0$ and of a tridiagonal-matrix perturbation…
We investigate electron transport inside a ring system composed of a quantum dot (QD) coupled to two Majorana bound states confined at the ends of a one-dimensional topological superconductor nanowire. By tuning the magnetic flux threading…
A combinatorial construction proves an identity for the product of the Pfaffian of a skew-symmetric matrix by the Pfaffian of one of its submatrices. Several applications of this identity are followed by a brief history of Pfaffians.
We demonstrate a topological classification of vortices in three dimensional time-reversal invariant topological superconductors based on superconducting Dirac semimetals with an s-wave superconducting order parameter by means of a pair of…
The possibility of inducing topological superconductivity with cuprate high-temperature superconductors (HTSC) is studied for various heterostructures. We first consider a ballistic planar junction between a HTSC and a metallic ferromagnet.…
The constraints of $BF$ topological gauge theories are used to construct Hamiltonians which are anti-commutators of the BRST and anti-BRST operators. Such Hamiltonians are a signature of Topological Quantum Field Theories (TQFT's). By…